Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Relaxation after quenches in systems with photon-mediated long-range interactions

Stefan Schütz, Simon B. Jäger, Giovanna Morigi

Published Dec 16, 2015• 1 citation
OpenAlex

Abstract

We theoretically characterize the semiclassical dynamics of an ensemble of atoms after a sudden quench across a driven-dissipative second-order phase transition. The atoms are driven by a laser and interact via conservative and dissipative long-range forces mediated by the photons of a single-mode cavity. These forces can cool the motion and, above a threshold value of the laser intensity, induce spatial ordering. We show that the relaxation dynamics following the quench exhibits a long prethermalizing behaviour which is first dominated by coherent long-range forces, and then by their interplay with dissipation. Remarkably, dissipation-assisted prethermalization is orders of magnitude longer than prethermalization due to the coherent dynamics. We show that it is associated with the creation of momentum-position correlations, which remain nonzero for even longer times than mean-field predicts. This implies that cavity cooling of an atomic ensemble into the selforganized phase can require longer time scales than the typical experimental duration. In general, these results demonstrate that noise and dissipation can substantially slow down the onset of thermalization in long-range interacting many-body systems.

Related papers

Dissipation-Assisted Prethermalization in Long-Range Interacting Atomic Ensembles

Stefan Schütz, Simon B. Jäger, Giovanna Morigi

We theoretically characterize the semiclassical dynamics of an ensemble of atoms after a sudden quench across a driven-dissipative second-order phase transition. The atoms are driven by a laser and interact via conservative and dissipative long-range forces mediated by the photons of a single-mode cavity. These forces can cool the motion and, above a threshold value of the laser intensity, induce spatial ordering. We show that the relaxation dynamics following the quench exhibits a long prethermalizing behavior which is first dominated by coherent long-range forces and then by their interplay with dissipation. Remarkably, dissipation-assisted prethermalization is orders of magnitude longer than prethermalization due to the coherent dynamics. We show that it is associated with the creation of momentum-position correlations, which remain nonzero for even longer times than mean-field predicts. This implies that cavity cooling of an atomic ensemble into the self-organized phase can require longer time scales than the typical experimental duration. In general, these results demonstrate that noise and dissipation can substantially slow down the onset of thermalization in long-range interacting many-body systems.

arXiv:1512.05243•Physical Review Letters•Aug 15, 2016•36 citations

Prethermalization of Atoms Due to Photon-Mediated Long-Range Interactions

Stefan Schütz, Giovanna Morigi

Atoms can spontaneously form spatially ordered structures in optical resonators when they are transversally driven by lasers. This occurs when the laser intensity exceeds a threshold value and results from the mechanical forces on the atoms associated with superradiant scattering into the cavity mode. We treat the atomic motion semiclassically and show that, while the onset of spatial ordering depends on the intracavity-photon number, the stationary momentum distribution is a Gaussian function whose width is determined by the rate of photon losses. Above threshold, the dynamics is characterized by two time scales: after a violent relaxation, the system slowly reaches the stationary state over time scales exceeding the cavity lifetime by several orders of magnitude. In this transient regime the atomic momenta form non-Gaussian metastable distributions, which emerge from the interplay between the long-range dispersive and dissipative mechanical forces of light. We argue that the dynamics of self-organization of atoms in cavities offers a test bed for studying the statistical mechanics of long-range interacting systems.

arXiv:1407.7842•Physical Review Letters•Nov 14, 2014•69 citations

Signatures of Prethermalization in a Quenched Cavity-Mediated Long-Range Interacting Fermi Gas

Zemao Wu, Jijie Fan, Xue Zhang +2 more

The coupling of ultracold quantum gases to an optical cavity provides an ideal system for studying the novel long-range interacting nonequilibrium dynamics. Here we report an experimental observation of the out-of-equilibrium dynamics of a degenerate Fermi gas in the cavity after quenching the pump strength over a superradiant quantum phase transition. The relaxation dynamics exhibits impressively different stages of a delay, violent relaxation, long-lifetime prethermalization, and slowly final thermalization due to the photon-mediated long-range interaction with dissipation. Importantly, we reveal that the lifetime of the system stayed on the prethermalization exhibits the superlinear scaling of the atom number. Furthermore, we show that the backaction of the superradiant cavity field on the gas causes the exchange of atoms between the normal and superradiant state in the early evolution and then induces the prethermalization. This work opens an avenue to explore complex nonequilibrium dynamics of the dissipatively long-range interacting Fermi gases.

Physical Review Letters•Dec 12, 2023•24 citations

Mean-field theory of atomic self-organization in optical cavities

Simon B. Jäger, Stefan Schütz, Giovanna Morigi

Photons mediate long-range optomechanical forces between atoms in high-finesse resonators, which can induce the formation of ordered spatial patterns. When a transverse laser drives the atoms, the system undergoes a second-order phase transition that separates a uniform spatial density from a Bragg grating maximizing scattering into the cavity and is controlled by the laser intensity. Starting from a Fokker-Planck equation describing the semiclassical dynamics of the $N$-atom distribution function, we systematically develop a mean-field model and analyze its predictions for the equilibrium and out-of-equilibrium dynamics. The validity of the mean-field model is tested by comparison with the numerical simulations of the $N$-body Fokker-Planck equation and by means of a Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. The mean-field theory predictions well reproduce several results of the $N$-body Fokker-Planck equation for sufficiently short times and are in good agreement with existing theoretical approaches based on field-theoretical models. The mean field, on the other hand, predicts thermalization time scales which are at least one order of magnitude shorter than the ones predicted by the $N$-body dynamics. We attribute this discrepancy to the fact that the mean-field ansatz discards the effects of the long-range incoherent forces due to cavity losses.

arXiv:1603.05148•Physical Review A•Aug 1, 2016•18 citations

Semiclassical theory of synchronization-assisted cooling

Simon B. Jäger, Minghui Xu, Stefan Schütz +2 more

We analyze the dynamics leading to radiative cooling of an atomic ensemble confined inside an optical cavity when the atomic dipolar transitions are incoherently pumped and can synchronize. Our study is performed in the semiclassical regime and assumes that cavity decay is the largest rate in the system dynamics. We identify three regimes characterizing the cooling. At first hot atoms are individually cooled by the cavity friction forces. After this stage, the atoms' center-of-mass motion is further cooled by the coupling to the internal degrees of freedom while the dipoles synchronize. In the latest stage dipole-dipole correlations are stationary and the center-of-mass motion is determined by the interplay between friction and dispersive forces due to the coupling with the collective dipole. We analyze this asymptotic regime by means of a mean-field model and show that the width of the momentum distribution can be of the order of the photon recoil. Furthermore, the internal excitations oscillate spatially with the cavity standing wave forming an antiferromagnetic-like order.

arXiv:1702.01561•Physical Review A•Jun 30, 2017•17 citations

Chaotic and quantum dynamics in driven-dissipative bosonic chains

Filippo Ferrari, Fabrizio Minganti, Camille Aron +1 more

Thermalization in quantum many-body systems typically unfolds over timescales governed by intrinsic relaxation mechanisms. Yet, its spatial aspect is less understood. We investigate this phenomenon in the nonequilibrium steady state (NESS) of a Bose-Hubbard chain subject to coherent driving and dissipation at its boundaries, a setup inspired by current designs in circuit quantum electrodynamics. The dynamical fingerprints of chaos in this NESS are probed using semiclassical out-of-time-order correlators within the truncated Wigner approximation. At intermediate drive strengths, we uncover a two-stage thermalization along the spatial dimension: phase coherence is rapidly lost near the drive, while amplitude relaxation occurs over much longer distances. This separation of scales gives rise to an extended hydrodynamic regime exhibiting anomalous temperature profiles, which we designate as a “prethermal” domain. At stronger drives, the system enters a nonthermal, non-chaotic finite-momentum condensate characterized by sub-Poissonian photon statistics and a spatially modulated phase profile, whose stability is undermined by quantum fluctuations. We explore the conditions underlying this protracted thermalization in space and argue that similar mechanisms are likely to emerge in a broad class of extended driven-dissipative systems. Thermalization in quantum many-body systems can unfold across space in surprising ways. The authors reveal nonequilibrium regimes in a driven-dissipative quantum chain, including a spatially emergent prethermal domain and a nonthermal condensate destabilized by quantum fluctuations, with broad implications for driven quantum platforms

arXiv:2409.12225•Communications Physics•Oct 16, 2025•9 citations
We theoretically characterize the semiclassical dynamics of an ensemble of atoms after a sudden quench across a driven-dissipative second-order phase transition. The atoms are driven by a laser and interact via conservative and dissipative long-range forces mediated by the photons of a single-mode cavity. These forces can cool the motion and, above a threshold value of the laser intensity, induce spatial ordering. We show that the relaxation dynamics following the quench exhibits a long prethermalizing behaviour which is first dominated by coherent long-range forces, and then by their interplay with dissipation. Remarkably, dissipation-assisted prethermalization is orders of magnitude longer than prethermalization due to the coherent dynamics. We show that it is associated with the creation of momentum-position correlations, which remain nonzero for even longer times than mean-field predicts. This implies that cavity cooling of an atomic ensemble into the selforganized phase can require longer time scales than the typical experimental duration. In general, these results demonstrate that noise and dissipation can substantially slow down the onset of thermalization in long-range interacting many-body systems.
We theoretically characterize the semiclassical dynamics of an ensemble of atoms after a sudden quench across a driven-dissipative second-order phase transition. The atoms are driven by a laser and interact via conservative and dissipative long-range forces mediated by the photons of a single-mode cavity. These forces can cool the motion and, above a threshold value of the laser intensity, induce spatial ordering. We show that the relaxation dynamics following the quench exhibits a long prethermalizing behavior which is first dominated by coherent long-range forces and then by their interplay with dissipation. Remarkably, dissipation-assisted prethermalization is orders of magnitude longer than prethermalization due to the coherent dynamics. We show that it is associated with the creation of momentum-position correlations, which remain nonzero for even longer times than mean-field predicts. This implies that cavity cooling of an atomic ensemble into the self-organized phase can require longer time scales than the typical experimental duration. In general, these results demonstrate that noise and dissipation can substantially slow down the onset of thermalization in long-range interacting many-body systems.
Atoms can spontaneously form spatially ordered structures in optical resonators when they are transversally driven by lasers. This occurs when the laser intensity exceeds a threshold value and results from the mechanical forces on the atoms associated with superradiant scattering into the cavity mode. We treat the atomic motion semiclassically and show that, while the onset of spatial ordering depends on the intracavity-photon number, the stationary momentum distribution is a Gaussian function whose width is determined by the rate of photon losses. Above threshold, the dynamics is characterized by two time scales: after a violent relaxation, the system slowly reaches the stationary state over time scales exceeding the cavity lifetime by several orders of magnitude. In this transient regime the atomic momenta form non-Gaussian metastable distributions, which emerge from the interplay between the long-range dispersive and dissipative mechanical forces of light. We argue that the dynamics of self-organization of atoms in cavities offers a test bed for studying the statistical mechanics of long-range interacting systems.
The coupling of ultracold quantum gases to an optical cavity provides an ideal system for studying the novel long-range interacting nonequilibrium dynamics. Here we report an experimental observation of the out-of-equilibrium dynamics of a degenerate Fermi gas in the cavity after quenching the pump strength over a superradiant quantum phase transition. The relaxation dynamics exhibits impressively different stages of a delay, violent relaxation, long-lifetime prethermalization, and slowly final thermalization due to the photon-mediated long-range interaction with dissipation. Importantly, we reveal that the lifetime of the system stayed on the prethermalization exhibits the superlinear scaling of the atom number. Furthermore, we show that the backaction of the superradiant cavity field on the gas causes the exchange of atoms between the normal and superradiant state in the early evolution and then induces the prethermalization. This work opens an avenue to explore complex nonequilibrium dynamics of the dissipatively long-range interacting Fermi gases.
Photons mediate long-range optomechanical forces between atoms in high-finesse resonators, which can induce the formation of ordered spatial patterns. When a transverse laser drives the atoms, the system undergoes a second-order phase transition that separates a uniform spatial density from a Bragg grating maximizing scattering into the cavity and is controlled by the laser intensity. Starting from a Fokker-Planck equation describing the semiclassical dynamics of the NNN-atom distribution function, we systematically develop a mean-field model and analyze its predictions for the equilibrium and out-of-equilibrium dynamics. The validity of the mean-field model is tested by comparison with the numerical simulations of the NNN-body Fokker-Planck equation and by means of a Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. The mean-field theory predictions well reproduce several results of the NNN-body Fokker-Planck equation for sufficiently short times and are in good agreement with existing theoretical approaches based on field-theoretical models. The mean field, on the other hand, predicts thermalization time scales which are at least one order of magnitude shorter than the ones predicted by the NNN-body dynamics. We attribute this discrepancy to the fact that the mean-field ansatz discards the effects of the long-range incoherent forces due to cavity losses.
We analyze the dynamics leading to radiative cooling of an atomic ensemble confined inside an optical cavity when the atomic dipolar transitions are incoherently pumped and can synchronize. Our study is performed in the semiclassical regime and assumes that cavity decay is the largest rate in the system dynamics. We identify three regimes characterizing the cooling. At first hot atoms are individually cooled by the cavity friction forces. After this stage, the atoms' center-of-mass motion is further cooled by the coupling to the internal degrees of freedom while the dipoles synchronize. In the latest stage dipole-dipole correlations are stationary and the center-of-mass motion is determined by the interplay between friction and dispersive forces due to the coupling with the collective dipole. We analyze this asymptotic regime by means of a mean-field model and show that the width of the momentum distribution can be of the order of the photon recoil. Furthermore, the internal excitations oscillate spatially with the cavity standing wave forming an antiferromagnetic-like order.
Thermalization in quantum many-body systems typically unfolds over timescales governed by intrinsic relaxation mechanisms. Yet, its spatial aspect is less understood. We investigate this phenomenon in the nonequilibrium steady state (NESS) of a Bose-Hubbard chain subject to coherent driving and dissipation at its boundaries, a setup inspired by current designs in circuit quantum electrodynamics. The dynamical fingerprints of chaos in this NESS are probed using semiclassical out-of-time-order correlators within the truncated Wigner approximation. At intermediate drive strengths, we uncover a two-stage thermalization along the spatial dimension: phase coherence is rapidly lost near the drive, while amplitude relaxation occurs over much longer distances. This separation of scales gives rise to an extended hydrodynamic regime exhibiting anomalous temperature profiles, which we designate as a “prethermal” domain. At stronger drives, the system enters a nonthermal, non-chaotic finite-momentum condensate characterized by sub-Poissonian photon statistics and a spatially modulated phase profile, whose stability is undermined by quantum fluctuations. We explore the conditions underlying this protracted thermalization in space and argue that similar mechanisms are likely to emerge in a broad class of extended driven-dissipative systems. Thermalization in quantum many-body systems can unfold across space in surprising ways. The authors reveal nonequilibrium regimes in a driven-dissipative quantum chain, including a spatially emergent prethermal domain and a nonthermal condensate destabilized by quantum fluctuations, with broad implications for driven quantum platforms